Verified solution · Exam P

SOA Exam P Sample Question #199 Solution

This Exam P sample reference tests Conditional Probability. The claim weights for the no-, moderate-, and heavy-lifting groups are 0.02, 0.04, and 0.02. Moderate or heavy lifting therefore accounts for 0.06 of the total 0.08 claim probability, giving 0.75, choice A.

Independent analysis by ActuaryProof · reviewed August 4, 2026

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Independent solution

How to solve this Conditional Probability question

Setup

Let N, M, and H denote the three lifting levels, and let C denote filing a claim.

\Pr(N)=0.40

\Pr(M)=0.50

\Pr(H)=0.10

Model

Form the joint probability of each lifting level together with a claim.

\Pr(N\cap C)=0.40(0.05)=0.02

\Pr(M\cap C)=0.50(0.08)=0.04

\Pr(H\cap C)=0.10(0.20)=0.02

Compute

Add the claim weights and normalize the two requested groups.

\Pr(C)=0.02+0.04+0.02=0.08

\Pr(M\cup H\mid C)=\frac{0.04+0.02}{0.08}=0.75

Answer

Three quarters of claimants come from the moderate- or heavy-lifting groups.

\boxed{0.75\quad\text{(A)}}

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Error diagnosis

Why the other letters tempt

These notes identify the calculation error associated with each wrong letter when that error is reproducible.

BThe value 0.81 would leave posterior probability 0.19 for no lifting. The verified no-lifting claim weight gives 0.02/0.08=0.25 instead.
CThe value 0.85 is approximately (0.08+0.20)/(0.05+0.08+0.20). That calculation adds conditional claim rates without weighting them by the group proportions.
DThe value 0.86 would leave posterior probability 0.14 for no lifting, understating the no-lifting joint claim weight.
EThe value 0.89 would leave only 0.11 posterior probability for no lifting. Bayes' normalization shows that the correct complement is 0.25.

Original practice · fully worked

Original variant: infer a source mix from an overall event rate

Service requests are classified as low, medium, or high complexity. Low-complexity requests form half of all requests. The high-complexity proportion is unknown, and the remainder are medium complexity. Escalation rates for the three classes are 2%, 5%, and 20%, respectively, while 5.6% of all requests are escalated. Given an escalation, calculate the probability that the request was high complexity.

A
0.028
B
0.056
C
0.140
D
0.360
E
0.500

Variant answer in brief

If h is the high-complexity proportion, total probability gives 0.035+0.15h=0.056, so h=0.14. The high-complexity escalation weight is 0.14(0.20)=0.028, which is half of all escalations, choice E.

Setup

Let h be the high-complexity proportion; then the medium-complexity proportion is 0.50-h.

\Pr(L)=0.50

\Pr(M)=0.50-h

\Pr(H)=h

Model

Use the stated overall escalation probability to determine the unknown mixture proportion.

0.50(0.02)+(0.50-h)(0.05)+h(0.20)=0.056

Compute

Solve for the high-complexity share, then apply Bayes' theorem.

0.035+0.15h=0.056

h=0.14

\Pr(H\mid E)=\frac{0.14(0.20)}{0.056}=0.50

Answer

Half of escalated requests are high complexity.

\boxed{0.500\quad\text{(E)}}

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ActuaryProof. “SOA Exam P Sample Question #199 — Verified Solution.” Verified 2026-07-31.

Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.

How to solve this Conditional Probability question

Setup

Model

Compute

Answer

All 718 Exam P sample solutions in syllabus order

Why the other letters tempt

Original variant: infer a source mix from an overall event rate

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam P solutions

Turn this solution into a complete study sequence

Cite this solution